Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
z=int(input())
d={}
i=1
while i*(i+1)/2<z:
    if d.get(i*(i+1)/2,0)==0:
        d[i*(i+1)/2]=1
    i+=1
c=1
while c*(c+1)/2<z:
    g=z-c*(c+1)/2
    if d.get(g,0)!=0 and d[g]==1 :
        print("YES")
        exit()
    c+=1
print("NO")